Question

Rewrite each equation in vertex form by completing the square. Then identify the vertex.

Answer 1

ANSWER

Vertex form

$f(x) = {( x + \frac{7}{2}) }^{2} - \frac{61}{4}$

Vertex:

$V( - \frac{7}{2} , - \frac{6 1}{4} )$

EXPLANATION

The given function is

$f(x) = {x}^{2} + 7x - 3$

Add and subtract the square of half the coefficient of x.

$f(x) = {x}^{2} + 7x + ( { \frac{7}{2} })^{2} - 3 + ( { \frac{7}{2} })^{2}$

The vertex form is

$f(x) = {( x + \frac{7}{2}) }^{2} - \frac{61}{4}$

The vertex is

$V( - \frac{7}{2} , - \frac{6 1}{4} )$

Answer 2

Answer:

The vertex form of the given equation is f(x) = (x+7/2)²+(-61/4)  where vertex is (-7/2,-61/4).

Step-by-step explanation:

We have given a quadratic equation in standard form.

f (x)=  x²+7x-3

We have to rewrite given equation in vertex form.

y  = a(x-h)²+k is vertex form of equation where (h,k) is vertex of equation.

We will use method of completing square to solve this.

Adding and subtracting  (7/2)²  to above equation, we have

f(x) =  x²+7x-3+(7/2)²-(7/2)²

f(x) = x²+7x+(7/2)²-3-(7/2)²

f(x) = (x+7/2)²-3-49/4

f(x) = (x+7/2)²+(-12-49)/4

f(x) = (x+7/2)²+(-61/4)

Hence, The vertex form of the given equation is f(x) = (x+7/2)²+(-61/4)  where vertex is (-7/2,-61/4).